Mutation testing involves making small changes to code to test whether tests can detect the changes, like changing a + b to a - b. Running mutation testing on a Calculator class that returns the sum of inputs initially generated 1 test but did not kill any mutants. After adding a test with specific inputs, mutation testing was run again and generated 1 test that killed 1 mutant, achieving 100% coverage. The document discusses using mutation testing to improve test quality and ensure tests can detect small code changes or faults.